Analysis and improvement of the Bancroft algorithm for GNSS satellite orbit determination

Satellite orbit information is crucial for ensuring that global navigation satellite systems (GNSSs) provide appropriate positioning, navigation and timing services. Typically, users can obtain access to orbit information of a specific accuracy level from navigation messages or precise ephemeris products. Without this information, a system will not be able to provide normal service. In response to this problem, initial orbit information of a certain level of precision must be obtained to support subsequent applications, such as broadcasting or precise ephemeris calculations, thereby ensuring the successful subsequent operation of the navigation system. One of two ways to calculate the initial orbit of a GNSS satellite is to utilize ground tracking stations to observe satellite vector information in the geocentric inertial system; the second way is to utilize GNSS range observations and known orbit information from other satellites. For the second approach, some researchers use the Bancroft algorithm combined with receiver clock offset to determine the initial orbit of GNSS satellites. Because this method requires an additional known receiver clock offset, we study the dependence of the Bancroft algorithm on clock offset in GNSS orbit determination. By assessing the impact of errors of different magnitude on the accuracy of the orbit results, we obtain experimental conclusions. After comprehensively analyzing various errors, we determine the accuracy level that the Bancroft algorithm can achieve for orbit determination without considering receiver clock correction. Dual-frequency and single-frequency pseudorange data from IGS stations are used in orbit determination experiments. When a small receiver clock offset is considered and no correction is made, the deviations in the calculated satellite positions in three dimensions are approximately 979.3 and 1118.1 meters (dual and single frequency); with a satellite clock offset, these values are approximately 928.8 and 1062.7 meters (dual and single frequency).

SAMPLE CLOCK OFFSET COMPENSATION IN THE FIFTH-GENERATION NEW RADIO UPLINK

Рассмотрена проблема коррекции искажений OFDM-сигнала, вызванных смещением частоты дискретизации сигнала в приемном и передающем устройствах системы сотовой связи пятого поколения. Предлагаемый метод компенсации смещения частоты дискретизации основывается на прямой коррекции искажений, вносимых в передаваемый сигнал наличием смещения, и не предполагает какой-либо оценки величины смещения. Метод предназначен для коррекции сигналов в восходящем канале системы сотовой связи пятого поколения и основывается на использовании референсных сигналов, рекомендованных стандартами 3GPP. Результаты численного моделирования показали, что использование предлагаемого метода позволяет повысить эффективность передачи данных по многолучевому радиоканалу более чем на 15% в широком диапазоне значений отношения сигнал/шум. 5G-NR, CP-OFDM, synchronization, sample clock offset, PUSCH. О The paper investigates the issue of sampling clock offset ( SCO) in the fifth generation new radio systems. Due to the imperfect SCO estimation methods, the correction methods relying on the SCO estimation are not perfect, so the proposed method directly corrects the effect of SCO without using any kind of estimation method. Our method is designed to correct the signals in the physical uplink shared channel (PUSCH). The method uses reference signals as recommended by the 3rd generation partnership project (3GPP) standards. The results of the numerical simulation show that the use of the proposed method increases the efficiency of data transmission over the multipath radio channel by more than 15% in a wide range of signal-to-noise ratio values.

A Novel Long Short-Term Memory Predicted Algorithm for BDS Short-Term Satellite Clock Offsets

The satellite clocks carried on the BeiDou navigation System (BDS) are a self-manufactured hydrogen clock and improved rubidium clock, and their on-orbit performance and stabilities are not as efficient as GPS and Galileo satellite clocks caused of the orbital diversity of the BDS and the complexity of the space operating environment. Therefore, the existing BDS clock product cannot guarantee the high accuracy demand for precise point positioning in real-time scenes while the communication link is interrupted. To deal with this problem, we proposed a deep learning-based approach for BDS short-term satellite clock offset modeling which utilizes the superiority of Long Short-Term Memory (LSTM) derived from Recurrent Neural Networks (RNN) in time series modeling, and we call it QPLSTM. The ultrarapid predicted clock products provided by IGS (IGU-P) and four widely used prediction methods (the linear polynomial, quadratic polynomial, gray system (GM (1,1)), and Autoregressive Integrated Moving Average (ARIMA) model) are selected to compare with the QPLSTM. The results show that the prediction residual is lower than clock products of IGU-P during 6-hour forecasting and the QPLSM shows a greater performance than the mentioned four models. The average prediction accuracy has improved by approximately 79.6, 69.2, 80.4, and 77.1% and 68.3, 52.7, 66.5, and 69.8% during a 30 min and 1-hour forecasting. Thus, the QPLSTM can be considered as a new approach to acquire high-precision satellite clock offset prediction.

Qubit-Based Clock Synchronization for QKD Systems Using a Bayesian Approach

Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users’ clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware. Previous qubit-based synchronization protocols sacrifice secure key either directly or indirectly, and all known qubit-based synchronization protocols do not efficiently use all publicly available information published by the users. Here, we introduce a Bayesian probabilistic algorithm that incorporates all published information to efficiently find the clock offset without sacrificing any secure key. Additionally, the output of the algorithm is a probability, which allows us to quantify our confidence in the synchronization. For demonstration purposes, we present a model system with accompanying simulations of an efficient three-state BB84 prepare-and-measure protocol with decoy states. We use our algorithm to exploit the correlations between Alice’s published basis and mean photon number choices and Bob’s measurement outcomes to probabilistically determine the most likely clock offset. We find that we can achieve a 95 percent synchronization confidence in only 4140 communication bin widths, meaning we can tolerate clock drift approaching 1 part in 4140 in this example when simulating this system with a dark count probability per communication bin width of 8×10−4 and a received mean photon number of 0.01.

A Method to Accelerate the Convergence of Satellite Clock Offset Estimation Considering the Time-Varying Code Biases

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior.

Impact of Attitude Model, Phase Wind-Up and Phase Center Variation on Precise Orbit and Clock Offset Determination of GRACE-FO and CentiSpace-1

Currently, low Earth orbit (LEO) satellites are attracting great attention in the navigation enhancement field because of their stronger navigation signal and faster elevation variation than medium Earth orbit (MEO) satellites. To meet the need for real-time and precise positioning, navigation and timing (PNT) services, the first and most difficult task is correcting errors in the process of precise LEO orbit and clock offset determination as much as possible. Launched in 29 September 2018, the CentiSpace-1 (CS01) satellite is the first experimental satellite of LEO-based navigation enhancement system constellations developed by Beijing Future Navigation Technology Co. Ltd. To analyze the impact of the attitude model, carrier phase wind-up (PWU) and phase center variation (PCV) on precise LEO orbit and clock offset in an LEO-based navigation system that needs extremely high precision, we not only select the CS01 satellite as a testing spacecraft, but also the Gravity Recovery and Climate Experiment Follow-On (GRACE-FO). First, the dual-frequency global positioning system (GPS) data are collected and the data quality is assessed by analyzing the performance of tracking GPS satellites, multipath errors and signal to noise ratio (SNR) variation. The analysis results show that the data quality of GRACE-FO is slightly better than CS01. With residual analysis and overlapping comparison, a further orbit quality improvement is possible when we further correct the errors of the attitude model, PWU and PCV in this paper. The final three-dimensional (3D) root mean square (RMS) of the overlapping orbit for GRACE-FO and CS01 is 2.08 cm and 1.72 cm, respectively. Meanwhile, errors of the attitude model, PWU and PCV can be absorbed partly in the clock offset and these errors can generate one nonnegligible effect, which can reach 0.02~0.05 ns. The experiment results indicate that processing the errors of the attitude model, PWU and PCV carefully can improve the consistency of precise LEO orbit and clock offset and raise the performance of an LEO-based navigation enhancement system.

Pair Nodes Clock Synchronization Algorithm Based on Kalman Filter for Underwater Wireless Sensor Networks

Time synchronization is the basis of many applications. Aiming at the limitations of the existing clock synchronization algorithms in underwater wireless sensor networks, we propose a pairwise synchronization algorithm called K-Sync, which is based on the Kalman filter. The algorithm does not need the assistance of the position sensor or the speed sensor, and the high time synchronization accuracy can be realized only by utilizing the time-stamps information in the process of message exchange. The K-Sync uses the general constraints of the motion characteristics of the sensor nodes to establish the recursive equations of the clock skew, clock offset, relative mobility velocity, and relative distance. At the same time, the time-stamps are viewed as the observation variables and the system observation equation is obtained. The K-Sync estimates the normalized clock skew and offset of the node via the Kalman filter to achieve high-precision clock synchronization between the two nodes. The simulation shows that the K-Sync has obvious advantages in the key indicators such as the estimated accuracy of clock skew and clock offset, convergence speed, etc. In addition, the K-Sync is more robust to a variety of underwater motion scenes.